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HUMAN AND SYSTEMS ENGINEERING:. Gentle Introduction to Particle Filtering. Sanjay Patil 1 and Ryan Irwin 2 Graduate research assistant 1 , REU undergrad 2 Human and Systems Engineering URL: www.isip.msstate.edu/publications/seminars/msstate/2005/particle /. Abstract. Particle Filtering:

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HUMAN AND SYSTEMS ENGINEERING:

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### HUMAN AND SYSTEMS ENGINEERING:

Gentle Introduction to Particle Filtering

Sanjay Patil1 and Ryan Irwin2

Human and Systems Engineering

URL: www.isip.msstate.edu/publications/seminars/msstate/2005/particle/

• Abstract

• Particle Filtering:

• Most conventional techniques for speech analysis are based on modeling signals as Gaussian Mixture Models in Hidden Markov Model based systems.

• To overcome the mismatched channel conditions, and/or significantly reduce the complexity of the models, Nonlinear approaches are expected to perform better than the conventional techniques.

• Particle filters, based on sequential Monte Carlo methods, is one such nonlinear methods.

• Particle filtering allows complete presentation of the posterior distribution of the states. Statistical estimates can be computed easily even in the presence of nonlinearities.

• Outline of Presentation

• Nonlinear Methods – necessity

• Drawing Samples from a Probability distribution. (introduce ‘Particle’)

• Sequential Monte Carlo Methods – necessity, different names – bootstrap, condensation algorithm, survival of the fittest.

• Steps in particle filtering (explaining the algorithm – block schematic)

• Actual example – (along with all the steps)

• Brief review and applications for tracking

• As can be applied to Speaker Verification

• Demo

• Drawing samples from a probability distribution function

• Concept of samples and its weights

200 samples

• Take p(x)=Gamma(4,1)

• Generate some random samples

• Plot basic approximation to pdf

• Each sample is called as ‘Particle’

500 samples

5000 samples

• Particle filtering -

• Condensation Algorithm

• Survival of the fittest

• Different Names –

• Sequential Monte Carlo filters

• Bootstrap filters

General Problem Statement – Filtering – estimation of the states

• Tracking the state (parameters or hidden variables) as it evolves over time

• Sequentially arriving (noisy and non-Gaussian) observations

• Idea is to have best possible estimate of hidden variables

• Particle filtering algorithm continue…

General two-stage Framework

(Prediction-Update stages)

• Assume that pdf p(xk-1 | y1:k-1) is available at time k -1.

• Prediction stage:

• This is the prior of the state at time k ( without the information on measurement). Thus, it is the probability of the the state given only the previous measurements

• Update stage:

• This is posterior pdf from predicted prior pdf and newly available measurement.

• Particle filtering algorithm step-by-step (1)

• Particle filtering step-by-step (2)

• Particle filtering step-by-step (3)

• Particle filtering step-by-step (4)

• Particle filtering step-by-step (5)

• Particle filtering step-by-step (6)

• Particle filtering - visualization

• Drawing samples

• Predicting next state

• Updating this state

• What is THIS STEP???

• Resampling….

• Sampling Importance Resample algorithm (necessity)

• Applications:

• All the applications are mostly tracking applications in different forms….

• Visual Tracking – e.g. human motion (body parts)

• Prediction of (financial) time series – e.g. mapping gold price, stocks

• Quality control in semiconductor industry

• Military Applications

• Target recognition from single or multiple images

• Guidance of missiles

• What is the application for IES NSF funded project –

• Time series estimation for speech signal (Java demo)

• Speaker Verification (details on next slide)

• Pattern Recognition Applet

• Java applet that gives a visual of algorithms implemented at IES

• Classification of Signals:

• PCA - Principle Component Analysis

• LDA - Linear Discrimination Analysis

• SVM - Support Vector Machines

• RVM - Relevance Vector Machines

• Tracking of Signals

• LP - Linear Prediction

• KF - Kalman Filtering

• PF – Particle Filtering

• Pattern Classification

• Different data sets need to be differentiated without looking at all the data samples

• Classifications distinguishes between sets of data without the samples

• Algorithms separate data sets with a line of discrimination

• To have zero error the line of discrimination should completely separate the classes

• These patterns are easy to classify

• Pattern Classification

• Toroidals are not classified very successfully with a straight line

• Error should be around 50% because half of each class is separated

• A proper line of discrimination of a toroidal would be a circle enclosing only the inside set

• Signal Tracking

• The input signals are now time based with the x-axis representing time

• All the signal tracking algorithms are implemented with interpolated data

• The interpolation ensures that the input samples are at regular intervals

• Sampling is always done on regular intervals

• The linear prediction algorithm is a linear way to predict signals with no noise

• Signal Tracking

• The Kalman filter and particle filter are based on prediction of the states of the signal

• States are related to the observations through the state equation

• The particle filtering algorithm introduces process and measurement noise

• At each iteration possible states are given by the black points

• The average of the black points is where the overall state is predicted to be

• References:

• S. Haykin and E. Moulines, "From Kalman to Particle Filters," IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, Pennsylvania, USA, March 2005.

• M.W. Andrews, "Learning And Inference In Nonlinear State-Space Models," Gatsby Unit for Computational Neuroscience, University College, London, U.K., December 2004.

• P.M. Djuric, J.H. Kotecha, J. Zhang, Y. Huang, T. Ghirmai, M. Bugallo, and J. Miguez, "Particle Filtering," IEEE Magazine on Signal Processing, vol 20, no 5, pp. 19-38, September 2003.

• N. Arulampalam, S. Maskell, N. Gordan, and T. Clapp, "Tutorial On Particle Filters For Online Nonlinear/ Non-Gaussian Bayesian Tracking," IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174-188, February 2002.

• R. van der Merve, N. de Freitas, A. Doucet, and E. Wan, "The Unscented Particle Filter," Technical Report CUED/F-INFENG/TR 380, Cambridge University Engineering Department, Cambridge University, U.K., August 2000.

• S. Gannot, and M. Moonen, "On The Application Of The Unscented Kalman Filter To Speech Processing," International Workshop on Acoustic Echo and Noise, Kyoto, Japan, pp 27-30, September 2003.

• J.P. Norton, and G.V. Veres, "Improvement Of The Particle Filter By Better Choice Of The Predicted Sample Set," 15th IFAC Triennial World Congress, Barcelona, Spain, July 2002.

• J. Vermaak, C. Andrieu, A. Doucet, and S.J. Godsill, "Particle Methods For Bayesian Modeling And Enhancement Of Speech Signals," IEEE Transaction on Speech and Audio Processing, vol 10, no. 3, pp 173-185, March 2002.